Problems on Trains

Train length = 544 m, time to cross pole = 16 seconds. Train speed = 544/16 = 34 m/s. Platform length = distance in 25 seconds = 34 × 25 = 850 m. Person crosses 850 m in 5 minutes 40 seconds = 340 seconds. Person's speed = 850/340 = 2.5 m/s.

Train A takes 4 hours (4am to 8am), Train B takes 3.5 hours (6am to 9:30am). Speed A = D/4, Speed B = D/3.5. At 6am, Train A has covered D/2 distance. Remaining D/2 distance covered at relative speed D/4 + D/3.5 = 15D/28. Time = (D/2)/(15D/28) = 14/15 hours = 56 minutes. They meet at 6:56am.

Total distance = 150 + 180 = 330 m. Time = 2.5 seconds. Relative speed = Distance/Time = 330/2.5 = 132 m/s. Since trains are moving in opposite directions, relative speed = Speed1 + Speed2. So 132 = 45 + Speed2, giving Speed2 = 87 m/s.

Speed = 36 km/hr = 10 m/s. Distance covered in 30 seconds = 10 × 30 = 300 meters. This distance equals train length + platform length. So 150 + platform length = 300, platform length = 150 meters.

Total distance = length of train + length of platform = (20 × 15 + 10) + 50 = 300 + 10 + 50 = 360m. Speed = 144 km/hr = 144 × 5/18 = 40 m/s. Time = Distance/Speed = 360/40 = 9 seconds. Option C (9) is correct. Key steps: convert speed to m/s, calculate total length (train + platform), then time = distance/speed.

The trains approach each other, so their relative speed is 40 + 60 = 100 km/hr. Time to meet = distance / relative speed = 800/100 = 8 hours. In 8 hours, the train from A travels 40 × 8 = 320 km from A. Therefore they cross 320 km from station A.

Relative speed = distance/time = 250/9 m/s = 100 km/hr. Person's speed = 60 km/hr, so goods train speed = 100 - 60 = 40 km/hr (speeds add in opposite directions).

Total distance to cover = 175 + 125 = 300 m in 10 seconds. Relative speed = 300/10 = 30 m/s = 108 km/h. Let second train's speed be v km/h. Then 30 + v = 108, so v = 78 km/h.

When trains move towards each other, their relative speed is the sum: 33 + 39 = 72 km/hr = 72 × (5/18) = 20 m/s. Total distance to cross = 125 + 115 = 240 m. Time = distance / speed = 240 / 20 = 12 seconds. This uses the concept of relative motion in opposite directions.

First train's speed = 150/15 = 10 m/s. When trains cross in opposite directions, relative speed = sum of speeds. Relative speed = (150+150)/12 = 25 m/s. Second train's speed = 25 - 10 = 15 m/s = 15 × 18/5 = 54 km/h. Option A would require 16.11 m/s, option C would need 15.56 m/s, option D would need 10 m/s.

Total distance to cross = 125 + 125 = 250m = 0.25 km. Time = 6 seconds = 6/3600 hr = 1/600 hr. Relative speed (opposite directions) = 0.25 ÷ (1/600) = 150 km/hr. Speed of other train = 150 - 65 = 85 km/hr. Option A (75 km/hr) would result from subtracting incorrectly.

Total distance to cover = 250 + 260 = 510 m. Relative speed (opposite direction) = 100 + 104 = 204 km/hr = 204 × (5/18) = 56.67 m/s. Time = distance/speed = 510/56.67 ≈ 9 seconds.

When trains travel in opposite directions, relative speed = sum of speeds = 75+50 = 125 km/hr = 125×(5/18) m/s. Total distance = sum of lengths = 175+200 = 375 m. Time = 375/(125×5/18) = 10.8 seconds. Option A forgets unit conversion, B is for same direction, D is incorrect.

Train length = 500 m, train speed = 63 km/h, man speed = 3 km/h (same direction). Relative speed = 63-3 = 60 km/h = 60×(5/18) = 50/3 m/s. Time = 500/(50/3) = 30 seconds. Options A, C, D are miscalculations or wrong relative speeds.

Total distance to cross the platform = length of train + length of platform = 420 + 180 = 600 metres. Time taken = 12 seconds. Speed in m/s = 600/12 = 50 m/s. Convert to km/hr: 50 × (18/5) = 180 km/hr. Option B is correct.